[SOLVED] Socga2332 – problem set 4

Instructions
1. Submit two files for each problem set. The first is a R Markdown (.Rmd) file that can be run without error from start to end. The second is a PDF rendered from your R Markdown file or created using LATEX.
2. Name your files following this convention: [Last Name]_ps1.Rmd and [Last Name]_ps1.pdf.
4. Comment on your code wherever possible and explain your ideas in detail. You will get credit for showing the steps you take and for explaining your reasoning, even if you do not get the correct final result.

Part 1: Fixed Effects and Random Effects Models
In this exercise, we will use the dataset sibling_data.dta to study the effect of mother experiencing stress in pregnancy on a child’s birth weight. All variables are described in the table below.
Variable Name Variable Detail
Group Variable householdid Unique household id; Siblings from the same household share the same household id
Dependent Variable birthwt birth weight measured in pounds
Independent Variable stress Whether or not mother experienced stress in pregnancy (Yes=1; No=0)
female Infant’s gender (Female=1; Male=0)
magebirth Mother’s Age at Birth
numsibling Number of Sibling
meduy Mother’s Years of Schooling
feduy Father’s Years of Schooling
1.[20pts] Import the dataset sibling_data.dta to your R environment. Including all independent variables, build an OLS model, a fixed effects model, and a random effects model (you can use the plm R package). Summarize regression results in a table. Make sure to label your models in your table (the column.labels argument in stargazer()).
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Hint: householdid is used as a grouping variable in your FE or RE model.
2.[5pts] Interpret the coefficient of stress in the OLS model.
3.[5pts] Interpret the coefficient of stress in the fixed effects model.
4.[5pts] Interpret the coefficient of magebirth in the fixed effects model.
5.[5pts] Perform a F-test to compare the OLS and the fixed effects models and interpret outputs (use pFtest from the plm R package).
6.[5pts] Compared to an OLS model, what are the benefits of using a fixed effects model?
7.[5pts] Why don’t we get coefficients of meduy, feduy, and numsibling in the fixed effects model?
8.[10pts] Why do we get coefficients of meduy, feduy, and numsibling in the random effects (random intercepts) model?
9.[10pts] How does the coefficient of stress change between (a) the OLS model and the fixed effects model and (b) the OLS model and the random effects model? What could be the potential causes that lead to these changes?
10.[10pts] Perform a Hausman test to compare fixed-effects and random-effects models (figure out how to use the phtest function from the plm R package; you might look into the help page and examples by typing
?plm::phtest into your console)
(a) What is the null hypothesis of this model? What is the alternative hypothesis?
(b) Is the null hypothesis rejected? Based on the test, which model would you use?
Hint: Hausman test evaluates whether the results (i.e. the estimated coefficients) from a fixed-effects and random-effects model are significantly different. You are encouraged to search online what the test is and how to decide which model is preferred.
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